Question

已知向量a=(sina,1),向量b=(cosa,2) a∈(0,π/4),（1） 若a‖b,求tana (2)若a·b

Answer 1

(1)若a‖b,则b=ka

即(cosa,2)=k(sina,1)=(ksina,k)

即k=2,cosa=ksina

tana=1/2

(2)a.b=(sina,1).(cosa,2)=sina*cosa+2=17/8

sin2a=1/4,cos2a=√[1-(1/4)^2]=√15/4

sin(2a+π/4)=sin2a*cos(π/4)+cos2a*sin(π/4)

=1/4*√2/2+√15/4*√2/2=(√2+√30)/8